In this paper, a deterministic model describing the dynamics of the in-host HIV infection of CD4+ T-cells is proposed. The model incorporates the presence of the CD8+ T-cells and two types of antiretroviral drugs, for disrupting new infection and for inhibiting virus production, respectively. First, the existence, boundedness and positivity of the model solutions are shown, the basic reproduction number R0 being then derived and shown to be a threshold value as far as the stability of the equilibria is concerned. When R0 < 1, the infection-free equilibrium point is globally stable, whereas when R0 > 1, the system is uniformly persistent and the infected equilibrium point is globally asymptotically stable. Further, we develop an optimal control model by taking the effect of the antiretroviral drugs to be control variables in order to minimize the HIV infection in different scenarios. By using Pontryagin’s Minimum Principle and solving the model numerically, the results show that each antiretroviral drug in isolation can play a key role in reducing the count of both infected CD4+ T-cells and HIV viruses. However, a combination of both drugs could reduce the in-host HIV infection more significantly.

中文翻译：

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抗逆转录病毒治疗的细胞内HIV感染模型的稳定性分析和优化控制

在本文中，描述了 CD4 的宿主内 HIV 感染动态的确定性模型+建议使用 T 细胞。该模型结合了 CD 的存在8+T 细胞和两种抗逆转录病毒药物，分别用于破坏新感染和抑制病毒产生。首先，显示模型解的存在性、有界性和正性，基本再生数R0然后导出并显示为就平衡稳定性而言的阈值。什么时候R0 < 1,无感染平衡点是全局稳定的，而当R0 > 1,该系统是一致持久的，并且受感染的平衡点是全局渐近稳定的。此外，我们通过将抗逆转录病毒药物的效果作为控制变量来开发最优控制模型，以最大限度地减少不同情况下的 HIV 感染。通过使用 Pontryagin 最小原理和数值求解模型，结果表明，每种抗逆转录病毒药物单独使用都可以在减少感染 CD4 的计数方面发挥关键作用。+T 细胞和 HIV 病毒。然而，两种药物的组合可以更显着地减少宿主体内的 HIV 感染。